Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #87771 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#87773 |
| Hall | C3×C52 ⋊ SD16 |
| Sylow | C52 ⋊ C3×SD16 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3)(4,5,6,8,7,9,10,11)(13,14)(15,16)(17,18,20,21,19);(5,8)(6,10)(9,11)(12,13,15,16,14)(18,19)(20,21)147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 275);